1. ## Inverse Laplace Formula

Dear MHF Residents,

I need the proof of the Laplace inversion formula
$f(t)=\displaystyle\frac{1}{2\pi\mathrm{i}}\display style\int_{\sigma-\mathrm{i}\infty}^{\sigma+\mathrm{i}\infty}F(z)\ma thrm{e}^{tz}\mathrm{d}z,$
where $\sigma$ is a sufficiently large real number, without using the Fourier transform.